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Discrete Mathematics CS 2610

Discrete Mathematics CS 2610. February 19, 2009. X. X+Y. Y. Logic Gates: the basic elements of circuits. Electronic circuits consist of so-called gates connected by wires. x. x. Inverter (NOT gate ). OR gate. x. xy. AND gate. y. Multiway Logical Gates.

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Discrete Mathematics CS 2610

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  1. Discrete Mathematics CS 2610 February 19, 2009

  2. X X+Y Y Logic Gates: the basic elements of circuits • Electronic circuits consist of so-called gates connected by wires x x Inverter (NOT gate) OR gate x xy AND gate y

  3. Multiway Logical Gates • Multiple Input AND, OR Gates x1 x1+x2+… + xn x2 xn x1 x1x2…  xn x2 xn

  4. Combinational Circuits • Combinational Circuits are circuits in which the logical gates’ outputs depend on their current inputs only • No loops • No memory capabilities • No current state worries

  5. Circuit Design • Design a circuit for xy + xy x y xy + xy

  6. F x y 0 0 1 0 1 0 1 0 0 1 1 1 Circuit Design • Design a circuit for xy + xy x y xy + xy

  7. F x y 0 0 0 0 1 1 1 0 1 1 1 0 Circuit Design: XOR Design a circuit that implements the XOR (the stairway lighting problem) xy + xy x y xy + xy

  8. Circuit Design (aside) up The stairway light switches: down up Switch 2 down up Switch 1 down + -

  9. Circuit Design • Design a circuit for xy + z

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